The creation of an acoustic pressure sensor having an output depending on the direction of the acoustic propagation requires the sensing of the acoustic pressure gradient. Currently, there are two approaches commonly used to achieve directional acoustic sensing. One approach consists of using a matched pair of non-directional microphones 102, 104 that sample the sound at two points separated by a distance, d 106, as shown in FIG. 1. The signals from these microphones are electronically processed to achieve the desired directivity. Another approach consists of constructing a single directional microphone 108 in which the two sides of the microphone diaphragm 110, 112 receive sound pressure from separate ports 115, 116 on the exterior, as shown in FIG. 2a. Typically, the sound from one port is delayed by a resistive material (not shown) to achieve a desired directivity.
Unfortunately, as the size of any directional sound pressure sensor is reduced, the difference in the two sensed pressures also diminishes. This means that in approaches employing two microphones, the difference in the signals becomes very small relative to the common mode or average pressure. This small difference is also very sensitive to small differences in the response characteristics of the microphones, hence there is a requirement for careful matching.
Because the spacing 118 between the sound ports in directional microphones is typically much smaller than the sound wavelength, the difference in the detected pressures also diminishes as the frequency decreases, or equivalently, as the wavelength increases.
FIG. 2b shows the measured frequency response of the Etymotic D-mic, a directional microphone used in hearing aids (not shown). The loss of sensitivity at low frequencies is shown in the curve labeled “Directional Microphone—Low Cut” 120 which is the uncompensated response of this microphone. This curve shows a 6 dB/octave high-pass filter characteristic typical of directional microphones. This response is typically compensated using a 6 dB/octave low-pass filter along with gain to achieve the “Flat” response shown in the “Directional Microphone—Flat” curve 122 of FIG. 2b. While such electronic compensation achieves the desirable frequency response, the roughly 30 dB of gain needed at low frequencies also dramatically amplifies the microphone self-noise. Therefore, the increase in noise and loss of sensitivity in miniature directional microphones limits their applicability and precludes their use in high-performance systems.
The directional acoustic sensing concepts described hereinabove are considered “first-order” differential microphones because they rely on an estimate of the pressure gradient through a measurement of the simple difference in pressure at two points. The directivity pattern of first-order differential microphones is the well-known figure eight pattern. The amplitude of the response is proportional to cos(θ), where θ is the propagation direction relative to the line that connects the pressure measurement points. If θ=π/2, the response will be at a minimum or a null. Along with the figure eight directivity pattern, it is common to either introduce a small delay in one of the pressure signals, or combine the pressure difference with a measurement of the pressure to obtain a wide range of first-order directivity patterns ranging from omnidirectional to cardioid or hypercardioid.
While first-order directional microphones have proven very beneficial in a large number of applications, there is great potential for dramatic improvements in performance through the use of second (and higher) order microphone systems. A second-order differential pressure sensing scheme can be schematically represented by the arrangement shown in FIG. 3. This system consists of three omnidirectional microphones 126, 128, 130, separated from each other by a distance, d 132. Microphones 126, 128, 130 generate output signals S1, S2, and S3, respectively. Two difference signals, S1−S2 and S3−S2 may be computed. The difference between these two difference signals is S1−2S2+S3. As shown below, while the output of a first-order pressure gradient sensor is proportional to cos(θ), the output of a second-order sensor is proportional to cos2(θ), giving a much stronger dependence on θ and, consequently, a much greater ability to reject unwanted sounds.
To illustrate the directivities and frequency responses of first- and second-order differential pressure sensors, assume that a plane harmonic wave of amplitude P having a frequency ω is propagating with speed c at an angle θ relative to the line connecting the microphones. If the location of S2 (i.e., the signal generated by microphone 128) is chosen to be the origin, then the pressures measured by the three microphones 126, 128, 130 in FIG. 3 may be expressed as S1=Pei(ωt+kd), S2=Peiωt, and S3=Pei(ωt−kd), where k=(ω/c)cos(θ). The output of the second-order sensor is then:S1−2S2+S3=Peiωt(eikd+e−ikd−2)=2Peiωt(cos(kd)−1)≈Peiωt(kd)2=Peiωtω2cos2(θ)(d/c)2   (1)
A first-order differential pressure sensor could be formed as in FIG. 1 where only the difference between S1 and S2 is taken:S1−S2=Peiωt(eikd−1)≈Peiωtikd=Peiωtiωcos(θ)(d/c)  (2)
The results of Equations (1) and (2) show the difference in the dependence on the angle of incidence, θ. The directivity patterns 134, 136 of first and second-order pressure gradient microphones, respectively, are compared in FIG. 4. By observing FIG. 4, it may be seen that the cos2(θ) dependence of the second-order sensor gives it better rejection of off-axis sounds (i.e., for angles other than zero or 180°) than the first-order sensor, which depends on cos(θ). This substantially sharper directivity pattern results in greatly enhanced rejection of unwanted signals.
While the directionality of higher-order differencing schemes can be significantly superior to those of first-order systems, several practical difficulties have hampered their application in commercial products. Along with the dramatic difference in directionality illustrated in Equations (1) and (2), it should also be readily observed that the two sensors have markedly different dependencies on the sound frequency, ω.
As may be seen in FIG. 2b, the frequency response of first-order directional microphones has a 6 dB/octave high-pass filter characteristic with a corner frequency that is equal to the first resonant frequency of the microphone diaphragm. This filter shape is due to the linear dependence on ω shown in Equation (2). The gain needed to compensate for the loss of low-frequency signals results in a substantial degradation in the noise performance of first-order microphones. Unfortunately, a second-order differential (or directional) microphone typically has a high-pass frequency response with a 12 dB/octave slope. This is because the second-order difference obtained in Equation (1) depends on ω2. The dramatic attenuation of low-frequency sounds often causes these signals to be lost in the noise of the system.
The predicted frequency responses of omnidirectional and first- and second-order differential microphones are compared in FIG. 5, curves 134, 136, and 138, respectively. These results assume that each microphone has a resonant frequency of 5 kHz (similar to the microphone used in the results shown in FIG. 2b. The responses are normalized so that they are unity (or zero dB) at the microphone's resonant frequency. FIG. 5 illustrates the dramatic loss of sensitivity of the second-order microphone at frequencies that are much below resonance.
In addition to the differences in directivity and frequency response of the first- and second-order pressure differences described in Equations (1) and (2), it is also apparent that as the size of the sensor diminishes, i.e., as d is reduced, the sensitivity of the second-order sensor suffers more than the first-order sensor. This is because d is linear in Equation 2 but is squared in Equation (1). This loss in sensitivity with diminishing size or aperture adds a further challenge to the design of miniature directional acoustic sensors.
In spite of the extreme challenges in overcoming the low sensitivity and poor frequency response of second-order microphones, the improvement in directivity depicted in FIG. 4 indicates there is a very substantial payoff if a practical design can be developed. One object of the present invention is to provide a silicon microphone diaphragm that achieves this.
The improvements in the technology of acoustic sensing provided by the present invention may have a profound impact on a number of industries. The ability to construct very small, low-cost acoustic sensors that are highly directional can result in dramatic performance improvements in products that deal with acoustic communication and will open doors to the creation of new, compact and low-cost devices that sense the location of sound sources.
One industry that may be significantly enhanced by this technology is the hearing aid industry. An extremely common complaint of hearing aid users continues to be that they have great difficulty understanding speech in noisy environments. Of all available technologies, the use of directional microphones has shown the most promise for addressing this problem. A number of clinical studies of the hearing impaired have demonstrated improvements in speech intelligibility in noise from the use of directional microphones. Despite the ample evidence that directional microphones play a crucial role, only very modest improvements in their performance have so far been observed. It is believed that many engineering challenges still stand in the way of directional microphones achieving their full potential.
Along with producing greatly improved devices for the hearing impaired, the present invention may also enable the development of other advanced consumer products such as directional microphones for telephones, computers, portable digital devices, camcorders, and surveillance systems. All of these products will benefit from the incorporation of miniature directional microphones.